Consider the reaction

Question

Zn(OH)2(s) + 2CN-(aq) <--> Zn(CN)2(s) + 2OH-(aq)

a) Calculate K for the reaction. (Ksp Zn(CN)2= 8.0 x 10^-12)
b) Will Zn(CN)2 precipitate if NaCN is added to a saturated Zn(OH)2 solution?

I tried splitting this into two equations:
Zn(OH)2(s)<--> Zn(CN)2(s) + 2OH-(aq)
2CN-(aq) <--> Zn(CN)2(s) + 2OH-(aq)
But that really doesn't work stoichiometrically. I think I know how to do the problem if water is a "product", but I'm not sure how to work it out this way.

Rxn 1:
Zn(OH)2 ==> Zn^+2 + 2 OH^- Ksp = ??

Rxn 2:
Zn(CN)2 ==> Zn^+2 + 2CN^- Ksp = xx

Reverse Rxn 2 for which K'sp = 1/Ksp.
Add Rxn 2 for which Ksp = ??

This will give you the reaction you want and Krxn = Ksp(rxn 1) x K'sp(reverse of rxn 2).
Post your work if you get stuck.

I have a Ksp value in my book for Zn(OH)2 that equals 4 x 10^-17. Is this fine to use or am I supposed to find that value in the problem? And would this number have (1) sig figs or is it a "known" value?

Also, would I be correct in thinking that Zn(CN)2 will precipitate when
NaCN is added to the saturated Zn(OH)2 solution, because the left side of the equation increased so the right must as well?

I have an VERY old text from the 70s that lists Ksp for Zn(OH)2 as 3.3E-17. Your value, then, probably is the more up to date one. And if it lists 4E-17 that is one significant figure. It is an experimentally determined (in some cases calculated) value. It is not a "known" value.

Yes, I would have thought that Ksp for Zn(OH)2 would have been quoted in the problem since Ksp for Zn(CN)2 is listed.

No, I don't think your thinking is correct on the precipitation part. Frankly, I'm not sure that question can be answered since no concentration of CN^- is given. Check your problem to make sure you didn't just skip that part when copying to this forum. You might have one ion and you might have 25 grams. But you can get some handle on it by calculating the concentration of Zn^+2 and the hydroxide ion in a saturated solution of Zn(OH)2, then calculating the concentration of CN^- required to ppt Zn(CN)2.